I've used the headset in the 737 for seven months now and love it. There are better ANR headsets out there, but all of them require batteries and I'm not willing to go that route.
There is a soft-sided carrying case (with padding) that has a handle, so theoretically you could attach it to your bag with a carabiner. That being said, I wouldn't do it just because I'd break the headset sooner or later. Plus, the headset barely fits inside the case and getting it in is a hassle.
I keep mine in a Rubbermaid container inside my flight bag.